Australia's ASX 200 ended down 0.23 percent, or 11.808 points, at 5,207.8, after opening up more than 1 percent, weighed by losses in the energy subindex, which was down 0.69 percent, and its financials sector, which fell 0.69 percent.

The Japanese benchmark index Nikkei 225 closed up 0.34 percent, or 56.12 points, at 16,729.04, off an earlier high of 16,787.06. South Korea's Kospi finished up 0.4 percent, or 7.88 points, at 1,999.36.

Mainland China markets were mixed; the Shanghai composite closed nearly flat up 0.06 percent, or 1.814 points, at 3,023.792 and the Shenzhen composite ended up 0.621 percent, or 12.277 points, at 1,989.334. In Hong Kong, the Hang Seng index was down 0.11 percent, as of 3:22 pm HK/SIN time.

On the economic data front, China released better-than-expected August data, with fixed-asset investment growth holding steady at 8.1 percent on-year, August industrial output rising 6.3 percent on-year and retail sales increasing by 10.6 percent on-year. The country is in the midst of a massive economic transition toward a more consumption-based and services-led economy.

"Chinese August activity data came in slightly ahead of forecasts, providing confirmation to the better tone of recent releases," Patrick Bennett, a strategist at CIBC Capital Markets, said in a note Tuesday. "Still, the results were near enough to expectations that market impact was and should remain muted."

Traders immediately cut the chances of a September Fed rate hike, pricing in just a 15 percent probability, down from 21 percent before Brainard's speech and from as high as 30 percent on Friday.

"I think there is a bit of a sigh of relief because a dovish Fed official came out and was dovish," said Anna Rathbun, director of research for CBIZ Retirement Plan Services, said of Brainard's impact on U.S. stocks. But she noted, "There is general nervousness within the market, despite what's going on today, about the effectiveness of central bank policy."

The Fed has now entered a blackout period until the Federal Open Market Committee's (FOMC) two-day meeting on September 20-21.

In company news, Samsung Electronics rebounded by 4.23 percent in Asian trade, after losses of 7 percent on Monday worth 16 trillion won ($14.3 billion), after reports that Samsung Group's de facto leader Jay Y. Lee will be taking a board seat. The South Korean company will also be selling its printer business to HP, in a acquisition deal valued at $1.05 billion.

ASX-listed Fortescue Metals was up 0.85 percent, retracing much of an initial more than 4 percent jump, after the company announced it would repay $700 million of its 2019 term loan, and save on annual interest valued at about $26 million.

Down under, Australia's August National Australia Bank (NAB) Business Confidence Survey showed that business conditions slowed for a second month, but confidence actually picked up after the central bank cut rates in August.

"Over the next 12 months, we think Softbank is likely to trade largely in line with Alibaba, Sprint and the yen, and much of the upside appears realized in the first two," Deutsche Bank analysts said in a Tuesday note.

Yoshikazu Tsuno | AFP | Getty Images

In currency markets, in the wake of Brainard's dovish speech, the U.S. dollar index, which measures the greenback against a basket of currencies, was trading at 95.258 as of 3:23 p.m. HK/SIN. Fading expectations for the Fed to hike rates this month likely weighted on the dollar.

The dollar/yen currency pair was trading at 101.94, falling below levels of around 102 from last week. The Australian dollar was trading at $0.7517, down from levels above $0.77 last week.

"The commodity bloc currencies have benefited from the retreat in U.S. rates on Monday, but, with the market long Australian dollar according to our metrics, the currency is likely to sell off more on bad news than it rallies on upside surprises," said Daniel Katzive, foreign-exchange strategist at BNP Paribas, in a Tuesday note.